Cracking the coding interview 6.2

There is an 8*8 chess board in which two diagnolly opposite corners have been cut off. you are given 31 dominos, and a single Domino can cover exactly two squares. can you use the 31 dominos to cover the entire board? Prove your answer.

 

Impossible: the checker's lattice is black and white, and the color of the diagonal corner is the same, and each Domino card covers 1 black 1 white at a time, so 31 cards cover 31 black and 31 White, it is actually 30 Black 32 white or 32 black 30 white, so it is impossible